It's partly a matter of taste and convention, but theory, attention to your objectives, and a smidgen of cognitive neuroscience [see the references] can provide some guidance.
Because a pdf and a cdf convey the same information, the distinction between them arises from how they do it: a pdf represents probability with areas while a cdf represents probability with (vertical) distances. Studies show that people compare distances faster and more accurately than they compare areas and that they systematically mis-estimate areas. Thus, if your purpose is to provide a graphical tool for reading off probabilities, your should favor using a cdf.
Pdfs and cdfs also represent probability density: the former does so by means of height while the latter represents density by slope. Now the tables are turned, because people are poor estimators of slope (which is the tangent of an angle; we tend to see the angle itself). Densities are good at conveying information about modes, heaviness of tails, and gaps. Favor using pdfs in such situations and anywhere else where local details of the probability distribution need to be emphasized.
Sometimes a pdf or cdf provides useful theoretical information. Its value (or rather the inverse thereof) is involved in formulas for standard errors for quantiles, extremes, and rank statistics. Display a pdf rather than a cdf in such situations. When studying multivariate correlations in a nonparametric setting, such as with copulas, the cdf turns out to be more useful (perhaps because it is the function that transforms a continuous probability law into a uniform one).
A pdf or cdf can be intimately associated with a particular statistical test. The Kolmogorov-Smirnov test (and the KS statistic) has a simple graphical representation in terms of a vertical buffer around the cdf; it has no simple graphical representation in terms of the pdf (that I know of).
The ccdf (complementary cdf) is used in special applications that focus on survivorship and rare events. Its use tends to be established by convention.
W.S. Cleveland (1994). The Elements of Graphing Data. Summit, NJ, USA: Hobart Press. ISBN 0-9634884-1-4
B.D. Dent (1999). Cartography: Thematic Map Design 5th Ed. Boston, MA, USA: WCB McGraw-Hill.
A.M. MacEachren (2004). How Maps Work. New York, NY, USA: The Guilford Press. ISBN 1-57230-040-X